2019独角兽企业重金招聘Python工程师标准>>> 
阶乘
在数学中，正整数的阶乘（英语：factorial）是所有小于及等于该数的正整数的积，计为n!
例如5的阶乘为5!，其值=120; 5!=5x4x3x2x1=120
用递归计算阶乘
一般数字的阶乘可以用递归的方法进行计算。
以下用递归计算1~12阶乘值；阶乘的值是以指数进行增长。
Sub Factorial_Main()
Dim num%, m%
Dim FactorNum&
With Sheet9
For num = 1 To 12
m = 5 + num
'if num>13 program will overflow
FactorNum = Factorial_Recursion(num)
.Cells(m, 1) = num
.Cells(m, 2) = FactorNum
Next num
End With
Debug.Print Timer
End Sub
'Factorial by Recursion Method
Function Factorial_Recursion(ByVal n)
If n <= 1 Then
Factorial_Recursion = 1
Exit Function
Else
Factorial_Recursion = n * Factorial_Recursion(n - 1)
End If
End Function
大数阶乘
一般阶乘的值都比较大，这时递归的方法不可行。此时需要用数组保存阶乘结果来进行计算。
思路：
1. 当前值乘以数组中的值
2. 将结果保存到数组中
3. 判断每个元素是否需要进位
4. 使用一个数组来保存阶乘每一位结果
以下是1~100的阶乘
具体代码如下：
'log10:https://baike.baidu.com/item/%E5%AF%B9%E6%95%B0%E5%87%BD%E6%95%B0/6013318?fr=aladdin
'Calculate the Carry
Function Carry_Bit(ByRef Bit, ByVal Pos)
Dim i&
Dim Carry
Carry = 0 'Initial
For i = 1 To Pos 'Check 1~Pos whether need carry bit
Bit(i) = Bit(i) + Carry 'Current value+Carry value
If Bit(i) <= 9 Then '<9 no need carray bit
Carry = 0
ElseIf Bit(i) > 9 And i < Pos Then '>9 but 9 And i >= Pos Then '>9 and highest digit
Do While Bit(i) > 9
Carry = Int(Bit(i) / 10) 'Save carry
Bit(i) = Bit(i) Mod 10 'one digit
i = i + 1
Bit(i) = Carry 'Save the carry
Loop
End If
Next i
Carry_Bit = Bit 'Return the Array
End Function
'Calculate multiple number factor
'Loop m
Sub Factorial_BigNumber_Multiple()
Dim num
Dim Digit, sum
Dim i, j
Dim Fact()
Dim Count, Str$
Dim m, n
With Sheet10
For m = 10 To 43
sum = 0: Digit = 0
num = .Cells(m, 10).Value 'Input Value
For i = 1 To num 'Calculate Result digit
sum = Log10(i) + sum
Next i
Digit = Int(sum) + 1 'Length of Data
ReDim Fact(1 To Digit) 'Allocate Array
For i = 1 To Digit 'Initial Array
Fact(i) = 0
Next i
Fact(1) = 1 'Setup 1st digit
For i = 1 To num 'Loop fact num
Pos = Highest_Digit(Fact, Digit) 'Record highest digit
For j = 1 To Pos
Fact(j) = Fact(j) * i 'fact(n-1)xN
Next j
Fact = Carry_Bit(Fact, Pos) 'process carry bit
Next i
Pos = Highest_Digit(Fact, Digit) 'Record highest digit
' m = 10
n = 12 'Initial
i = Pos
Str = "'"
Count = 0
Do While i <= Pos And i >= 1
Count = Count + 1
Str = Str & Fact(i)
If Count Mod 5 = 0 Then
.Cells(m, n) = Str
Str = "'"
n = n + 1
End If
If i = 1 And Str <> "" Then .Cells(m, n) = Str
i = i - 1
Loop
.Cells(m, 11) = Count
Next m
End With
Debug.Print Timer
End Sub
'Find Hightest digit
Function Highest_Digit(Arr, n)
Dim i
For i = n To 1 Step -1
If Arr(i) <> 0 Then
Highest_Digit = i
Exit Function
End If
Next i
End Function
'Function for Log10
Function Log10(ByVal x) As Double
Dim nLog10
nLog10 = Log(x) / Log(10)
Log10 = nLog10
End Function